A right star operation is a function from \(W\)  to \(W\)  partially defined with respect to a pair of noncommuting
generators \(I=\lbrace s,t\rbrace \subseteq S\) . Let \(m=m(s,t)\)  and consider the parabolic subgroup \(W_I=\langle s,t\rangle \) . Then each element
\(w\)  in \(W\)  admits a unique reduced factorization \(w=w^I \cdot w_I\)  where \(\mathcal {R}{(w^I)}\cap I = \emptyset \)  and
\(w_I\in W_I\) . This factorization is the left coset decomposition of \(w\)  with respect to \(I\) ; see [1]}. Depending on the value of \(w_I\) , one of the following mutually exclusive conditions must hold; the
sequences in (2) and (3) are both infinite if \(m=\infty \) .
